
1) Botanical shoot 2) Offset 3) Plant offshoot 4) Plant organ 5) Plant runner 6) Rhizome 7) Runner 8) Runner on a plant 9) Strawberry vine 10) Trailing branch of a plant 11) Underground runner 12) Underground stem 
Found on 
https://www.crosswordclues.com/clue/stolon

• (n.) A trailing branch which is disposed to take root at the end or at the joints; a stole. • (n.) An extension of the integument of the body, or of the body wall, from which buds are developed, giving rise to new zooids, and thus forming a compound animal in which the zooids usually remain united by the stolons. Such stolons are often ...
Found on 
http://thinkexist.com/dictionary/meaning/stolon/

An above-ground stem capable of growing a new plant.
Found on 
http://www.americantrails.org/

An above ground creeping stem, sometimes known as a runner.
Found on 
http://www.botanicalkeys.co.uk/flora/content/glossary.html

(from the article `reproductive system, plant`) The vegetative, or somatic, organs of plants may, in their entirety, be modified to serve as organs of reproduction. In this category belong such ... in biology, a special slender horizontal branch serving to propagate the organism. In botany a stolonalso called a runneris a s...
Found on 
http://www.britannica.com/eb/a-z/s/165

(from the article `stolon`) ...called a runneris a slender stem that grows horizontally along the ground, giving rise to roots and aerial (vertical) branches at specialized ... ...germinate, their archaeocytes emerge through an opening (micropyle), the various cellular types differentiate, and a new sponge grows. Other ... [2 r...
Found on 
http://www.britannica.com/eb/a-z/s/165

A branch that grows horizontally above the medium and produces roots and shoots at the nodes.
Found on 
http://www.clanorchids.com/clanglos.htm

A ground-lying or trailing stem that produces roots at the nodes. ... (09 Oct 1997) ... 
Found on 
http://www.encyclo.co.uk/local/20973

A horizontal stem lying on the surface of the soil.
Found on 
http://www.encyclo.co.uk/local/22037

A horizontal stem lying on the surface of the soil.
Found on 
http://www.encyclo.co.uk/local/22038

an above-ground, horizontal stem.
Found on 
http://www.encyclo.co.uk/local/22043

A modified, creeping, above-ground stem capable of rooting and sending up new shoots at its nodes, as in the strawberry plant..  Stolinferous; bearing stolons or runners or shoots that take root.
Found on 
http://www.encyclo.co.uk/visitor-contributions.php
 Sto'lon  noun
Sto'lon  noun [ Latin 
 stolo , 
 - onis : confer French 
 stolon . Confer 
 Stole a stolon, 1st 
 Stool .] 
 1.  (Botany) A trailing branch which is disposed to take root at the end or at the joints; a stole.  
 2.  (Zoology) An extension of the integu...
Found on 
http://www.encyclo.co.uk/webster/S/202

A shoot that bends to the ground and takes root; more commonly, a horizontal stem at or below surface of the ground that gives rise to a new plant at its tip.
Found on 
http://www.gardenology.org/wiki/Glossary_of_Gardening_Terms

A branch that grows horizontally above the medium and produces roots and shoots at the nodes.
Found on 
http://www.orchidplantcare.info/orchid-glossary/

An above ground spreading stem or runner that often produces a new plant at the tip. (example: Strawberry plants)
Found on 
http://www.thegardenhelper.com/dictionary.html

An aboveground stem that reclines or becomes prostrate and may form roots where nodes come into contact with the ground.
Found on 
https://extension.umd.edu/hgic/resource-library/vegetable-gardening-glossar

A stem running horizontally on the soil surface which may produce shoots or roots. See also Rhizome.
Found on 
https://www.encyclo.co.uk/local/20496
 runner noun
runner noun a horizontal branch from the base of plant that produces new plants from buds at its tips
Found on 
https://www.encyclo.co.uk/local/20974

A horizontal, fleshy aboveground stem or runner. Creeping grasses spread by rhizomes or stolons.
Found on 
https://www.encyclo.co.uk/local/22486

A runner or rootstock used to propagate (usually used for grasses).
Found on 
https://www.encyclo.co.uk/local/22488

A stolon is a horizontal stem growing above ground that forms roots at its tip.
Found on 
https://www.encyclo.co.uk/local/23353

A stolon is a horizontal stem growing above ground that forms roots at its tip.
Found on 
https://www.encyclo.co.uk/local/23362

a prostrate stem, at or just below the surface of the ground, that produces new plants from buds at its tips or nodes. · a rootlike extension of the body wall in a compound organism, as a bryozoan, usually giving rise to new members by budding.
Found on 
https://www.infoplease.com/dictionary/stolon

A horizontal, fleshy aboveground stem or runner. Creeping grasses spread by rhizomes or stolons.
Found on 
https://www.lowes.com/projects/lawn-and-garden/garden-glossary/project
  No exact match found.