Maximal trees.

We show that, consistently, there can be maximal subtrees of P(ω)<inline-graphic></inline-graphic> and P(ω)/fin<inline-graphic></inline-graphic> of arbitrary regular uncountable size below the size of the continuum c<inline-graphic></inline-graphic>. We also show that there are no maximal subtrees of P(ω)/fin<inline-graphic></inline-graphic> with countable levels. Our results answer several questions of Campero-Arena et al. (Fund Math 234:73-89, 2016). [ABSTRACT FROM AUTHOR]