given that micro tubules are involved in so many processes in cells, it seems that such a complex "highway" would require some advanced underlying mechanism to orchestrate its assembly in a direction needed for the cell, such as towards a kinetochore. multiple search results on google and textbooks simply just state polymerization as is without explaining how these events happen. so how are microtubules polymerized and how is this polymerization oriented directionally ?
Microtubules are made up by $\alpha$- and $\beta$-tubulin units, the wiki page for this will link you to a short section on microtubule dynamics, which is the basis of how the growth & shrinking of microtubules is controlled:
Microtubules grow (by addition of $\alpha\beta$-units) and shrink (by dissociation of these units) primarily at the '+ end', which is the one in the cell periphery not at the centriole. Actually both of these reactions (growing/polymerisation and shrinking/de-polymerisation) usually happen at the same time but with different speeds. These speeds depend on whether GDP or GTP is bound by the $\beta$-tubulin at the + end, the (relative) concentration of GTP-bound free monomers and other structural proteins. Except for the GTP/GDP bound state in the mircotubule all of these factors can be controlled (or altered) by the cell through various mechanisms (some are listed on the 2nd wiki page I linked; I may add some specific ones if I have more time).