Step 1: Understanding the Concept
Starch is a mixture of two polysaccharides, amylose and amylopectin. Both are made of \(\alpha\)-glucose.
Step 2: Compare the polymers
Amylose is an unbranched chain with only \(\alpha\)-1,4 links.
Amylopectin has main chains of \(\alpha\)-1,4 links with branches attached through \(\alpha\)-1,6 links.
Cellulose has \(\beta\)-1,4 links between \(\beta\)-glucose units.
Step 3: Conclusion
The description with \(\alpha\)-1,6 branching matches amylopectin. Starch is a mixture, so it is not the single polymer described.
Final Answer:
The polymer is amylopectin.
\[ \boxed{\text{(B) }\text{Amylopectin}} \]