Constructal theory, now called constructal law, has influenced and driven a significant amount of research and attention over the past 2 decades due to its significance in understanding designs found in nature. It is worth to remember that the origins of constructal law can be traced back to the design of heat conduction paths, alternatively called access problem, in Bejan's 1996 paper. However, it is evident that although branching designs are generated, geometric and 'constructal' constraints are always present and often not relaxed in their designs. In this paper, additional design explorations to solutions for the access problem are sought and discussed. Density based topology optimization under 6 different, tunable material interpolation models are chosen since design explorations can be considered to be straightforward for finding solutions and the design process is relaxed. The variation in the material property model highlights the importance of search spaces in any design process. To give fair comparisons, the final designs obtained from the optimization process are projected as 0-1 designs. The results reveal other topologies that perform better as compared to two constructal design cases. The significant difference starting from the fundamentals of constructal designs is also discussed. (C) 2016 Elsevier Ltd. All rights reserved.